TESTING/EIG/cchkst.f(3)

NAME
TESTING/EIG/cchkst.f

SYNOPSIS

  Functions/Subroutines
subroutine cchkst (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, ap, sd, se, d1, d2, d3, d4, d5, wa1, wa2, wa3, wr, u, ldu, v, vp, tau, z, work, lwork, rwork, lrwork, iwork, liwork, result, info)
CCHKST

Function/Subroutine Documentation

  subroutine cchkst (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, real thresh, integer nounit, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) ap, real, dimension( * ) sd, real, dimension( * ) se, real, dimension( * ) d1, real, dimension( * ) d2, real, dimension( * ) d3, real, dimension( * ) d4, real, dimension( * ) d5, real, dimension( * ) wa1, real, dimension( * ) wa2, real, dimension( * ) wa3, real, dimension( * ) wr, complex, dimension( ldu, * ) u, integer ldu, complex, dimension( ldu, * ) v, complex, dimension( * ) vp, complex, dimension( * ) tau, complex, dimension( ldu, * ) z, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, real, dimension( * ) result, integer info)

CCHKST

Purpose:

    !>
    !> CCHKST  checks the Hermitian eigenvalue problem routines.
    !>
    !>    CHETRD factors A as  U S U* , where * means conjugate transpose,
    !>    S is real symmetric tridiagonal, and U is unitary.
    !>    CHETRD can use either just the lower or just the upper triangle
    !>    of A; CCHKST checks both cases.
    !>    U is represented as a product of Householder
    !>    transformations, whose vectors are stored in the first
    !>    n-1 columns of V, and whose scale factors are in TAU.
    !>
    !>    CHPTRD does the same as CHETRD, except that A and V are stored
    !>    in  format.
    !>
    !>    CUNGTR constructs the matrix U from the contents of V and TAU.
    !>
    !>    CUPGTR constructs the matrix U from the contents of VP and TAU.
    !>
    !>    CSTEQR factors S as  Z D1 Z* , where Z is the unitary
    !>    matrix of eigenvectors and D1 is a diagonal matrix with
    !>    the eigenvalues on the diagonal.  D2 is the matrix of
    !>    eigenvalues computed when Z is not computed.
    !>
    !>    SSTERF computes D3, the matrix of eigenvalues, by the
    !>    PWK method, which does not yield eigenvectors.
    !>
    !>    CPTEQR factors S as  Z4 D4 Z4* , for a
    !>    Hermitian positive definite tridiagonal matrix.
    !>    D5 is the matrix of eigenvalues computed when Z is not
    !>    computed.
    !>
    !>    SSTEBZ computes selected eigenvalues.  WA1, WA2, and
    !>    WA3 will denote eigenvalues computed to high
    !>    absolute accuracy, with different range options.
    !>    WR will denote eigenvalues computed to high relative
    !>    accuracy.
    !>
    !>    CSTEIN computes Y, the eigenvectors of S, given the
    !>    eigenvalues.
    !>
    !>    CSTEDC factors S as Z D1 Z* , where Z is the unitary
    !>    matrix of eigenvectors and D1 is a diagonal matrix with
    !>    the eigenvalues on the diagonal ('I' option). It may also
    !>    update an input unitary matrix, usually the output
    !>    from CHETRD/CUNGTR or CHPTRD/CUPGTR ('V' option). It may
    !>    also just compute eigenvalues ('N' option).
    !>
    !>    CSTEMR factors S as Z D1 Z* , where Z is the unitary
    !>    matrix of eigenvectors and D1 is a diagonal matrix with
    !>    the eigenvalues on the diagonal ('I' option).  CSTEMR
    !>    uses the Relatively Robust Representation whenever possible.
    !>
    !> When CCHKST is called, a number of matrix  () and a
    !> number of matrix  are specified.  For each size ()
    !> and each type of matrix, one matrix will be generated and used
    !> to test the Hermitian eigenroutines.  For each matrix, a number
    !> of tests will be performed:
    !>
    !> (1)     | A - V S V* | / ( |A| n ulp ) CHETRD( UPLO='U', ... )
    !>
    !> (2)     | I - UV* | / ( n ulp )        CUNGTR( UPLO='U', ... )
    !>
    !> (3)     | A - V S V* | / ( |A| n ulp ) CHETRD( UPLO='L', ... )
    !>
    !> (4)     | I - UV* | / ( n ulp )        CUNGTR( UPLO='L', ... )
    !>
    !> (5-8)   Same as 1-4, but for CHPTRD and CUPGTR.
    !>
    !> (9)     | S - Z D Z* | / ( |S| n ulp ) CSTEQR('V',...)
    !>
    !> (10)    | I - ZZ* | / ( n ulp )        CSTEQR('V',...)
    !>
    !> (11)    | D1 - D2 | / ( |D1| ulp )        CSTEQR('N',...)
    !>
    !> (12)    | D1 - D3 | / ( |D1| ulp )        SSTERF
    !>
    !> (13)    0 if the true eigenvalues (computed by sturm count)
    !>         of S are within THRESH of
    !>         those in D1.  2*THRESH if they are not.  (Tested using
    !>         SSTECH)
    !>
    !> For S positive definite,
    !>
    !> (14)    | S - Z4 D4 Z4* | / ( |S| n ulp ) CPTEQR('V',...)
    !>
    !> (15)    | I - Z4 Z4* | / ( n ulp )        CPTEQR('V',...)
    !>
    !> (16)    | D4 - D5 | / ( 100 |D4| ulp )       CPTEQR('N',...)
    !>
    !> When S is also diagonally dominant by the factor gamma < 1,
    !>
    !> (17)    max | D4(i) - WR(i) | / ( |D4(i)| omega ) ,
    !>          i
    !>         omega = 2 (2n-1) ULP (1 + 8 gamma**2) / (1 - gamma)**4
    !>                                              SSTEBZ( 'A', 'E', ...)
    !>
    !> (18)    | WA1 - D3 | / ( |D3| ulp )          SSTEBZ( 'A', 'E', ...)
    !>
    !> (19)    ( max { min | WA2(i)-WA3(j) | } +
    !>            i     j
    !>           max { min | WA3(i)-WA2(j) | } ) / ( |D3| ulp )
    !>            i     j
    !>                                              SSTEBZ( 'I', 'E', ...)
    !>
    !> (20)    | S - Y WA1 Y* | / ( |S| n ulp )  SSTEBZ, CSTEIN
    !>
    !> (21)    | I - Y Y* | / ( n ulp )          SSTEBZ, CSTEIN
    !>
    !> (22)    | S - Z D Z* | / ( |S| n ulp )    CSTEDC('I')
    !>
    !> (23)    | I - ZZ* | / ( n ulp )           CSTEDC('I')
    !>
    !> (24)    | S - Z D Z* | / ( |S| n ulp )    CSTEDC('V')
    !>
    !> (25)    | I - ZZ* | / ( n ulp )           CSTEDC('V')
    !>
    !> (26)    | D1 - D2 | / ( |D1| ulp )           CSTEDC('V') and
    !>                                              CSTEDC('N')
    !>
    !> Test 27 is disabled at the moment because CSTEMR does not
    !> guarantee high relatvie accuracy.
    !>
    !> (27)    max | D6(i) - WR(i) | / ( |D6(i)| omega ) ,
    !>          i
    !>         omega = 2 (2n-1) ULP (1 + 8 gamma**2) / (1 - gamma)**4
    !>                                              CSTEMR('V', 'A')
    !>
    !> (28)    max | D6(i) - WR(i) | / ( |D6(i)| omega ) ,
    !>          i
    !>         omega = 2 (2n-1) ULP (1 + 8 gamma**2) / (1 - gamma)**4
    !>                                              CSTEMR('V', 'I')
    !>
    !> Tests 29 through 34 are disable at present because CSTEMR
    !> does not handle partial spectrum requests.
    !>
    !> (29)    | S - Z D Z* | / ( |S| n ulp )    CSTEMR('V', 'I')
    !>
    !> (30)    | I - ZZ* | / ( n ulp )           CSTEMR('V', 'I')
    !>
    !> (31)    ( max { min | WA2(i)-WA3(j) | } +
    !>            i     j
    !>           max { min | WA3(i)-WA2(j) | } ) / ( |D3| ulp )
    !>            i     j
    !>         CSTEMR('N', 'I') vs. CSTEMR('V', 'I')
    !>
    !> (32)    | S - Z D Z* | / ( |S| n ulp )    CSTEMR('V', 'V')
    !>
    !> (33)    | I - ZZ* | / ( n ulp )           CSTEMR('V', 'V')
    !>
    !> (34)    ( max { min | WA2(i)-WA3(j) | } +
    !>            i     j
    !>           max { min | WA3(i)-WA2(j) | } ) / ( |D3| ulp )
    !>            i     j
    !>         CSTEMR('N', 'V') vs. CSTEMR('V', 'V')
    !>
    !> (35)    | S - Z D Z* | / ( |S| n ulp )    CSTEMR('V', 'A')
    !>
    !> (36)    | I - ZZ* | / ( n ulp )           CSTEMR('V', 'A')
    !>
    !> (37)    ( max { min | WA2(i)-WA3(j) | } +
    !>            i     j
    !>           max { min | WA3(i)-WA2(j) | } ) / ( |D3| ulp )
    !>            i     j
    !>         CSTEMR('N', 'A') vs. CSTEMR('V', 'A')
    !>
    !> The  are specified by an array NN(1:NSIZES); the value of
    !> each element NN(j) specifies one size.
    !> The  are specified by a logical array DOTYPE( 1:NTYPES );
    !> if DOTYPE(j) is .TRUE., then matrix type  will be generated.
    !> Currently, the list of possible types is:
    !>
    !> (1)  The zero matrix.
    !> (2)  The identity matrix.
    !>
    !> (3)  A diagonal matrix with evenly spaced entries
    !>      1, ..., ULP  and random signs.
    !>      (ULP = (first number larger than 1) - 1 )
    !> (4)  A diagonal matrix with geometrically spaced entries
    !>      1, ..., ULP  and random signs.
    !> (5)  A diagonal matrix with  entries 1, ULP, ..., ULP
    !>      and random signs.
    !>
    !> (6)  Same as (4), but multiplied by SQRT( overflow threshold )
    !> (7)  Same as (4), but multiplied by SQRT( underflow threshold )
    !>
    !> (8)  A matrix of the form  U* D U, where U is unitary and
    !>      D has evenly spaced entries 1, ..., ULP with random signs
    !>      on the diagonal.
    !>
    !> (9)  A matrix of the form  U* D U, where U is unitary and
    !>      D has geometrically spaced entries 1, ..., ULP with random
    !>      signs on the diagonal.
    !>
    !> (10) A matrix of the form  U* D U, where U is unitary and
    !>      D has  entries 1, ULP,..., ULP with random
    !>      signs on the diagonal.
    !>
    !> (11) Same as (8), but multiplied by SQRT( overflow threshold )
    !> (12) Same as (8), but multiplied by SQRT( underflow threshold )
    !>
    !> (13) Hermitian matrix with random entries chosen from (-1,1).
    !> (14) Same as (13), but multiplied by SQRT( overflow threshold )
    !> (15) Same as (13), but multiplied by SQRT( underflow threshold )
    !> (16) Same as (8), but diagonal elements are all positive.
    !> (17) Same as (9), but diagonal elements are all positive.
    !> (18) Same as (10), but diagonal elements are all positive.
    !> (19) Same as (16), but multiplied by SQRT( overflow threshold )
    !> (20) Same as (16), but multiplied by SQRT( underflow threshold )
    !> (21) A diagonally dominant tridiagonal matrix with geometrically
    !>      spaced diagonal entries 1, ..., ULP.
    !>

Parameters
    NSIZES

    !>          NSIZES is INTEGER
    !>          The number of sizes of matrices to use.  If it is zero,
    !>          CCHKST does nothing.  It must be at least zero.
    !>

    NN

    !>          NN is INTEGER array, dimension (NSIZES)
    !>          An array containing the sizes to be used for the matrices.
    !>          Zero values will be skipped.  The values must be at least
    !>          zero.
    !>

    NTYPES

    !>          NTYPES is INTEGER
    !>          The number of elements in DOTYPE.   If it is zero, CCHKST
    !>          does nothing.  It must be at least zero.  If it is MAXTYP+1
    !>          and NSIZES is 1, then an additional type, MAXTYP+1 is
    !>          defined, which is to use whatever matrix is in A.  This
    !>          is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
    !>          DOTYPE(MAXTYP+1) is .TRUE. .
    !>

    DOTYPE

    !>          DOTYPE is LOGICAL array, dimension (NTYPES)
    !>          If DOTYPE(j) is .TRUE., then for each size in NN a
    !>          matrix of that size and of type j will be generated.
    !>          If NTYPES is smaller than the maximum number of types
    !>          defined (PARAMETER MAXTYP), then types NTYPES+1 through
    !>          MAXTYP will not be generated.  If NTYPES is larger
    !>          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
    !>          will be ignored.
    !>

    ISEED

    !>          ISEED is INTEGER array, dimension (4)
    !>          On entry ISEED specifies the seed of the random number
    !>          generator. The array elements should be between 0 and 4095;
    !>          if not they will be reduced mod 4096.  Also, ISEED(4) must
    !>          be odd.  The random number generator uses a linear
    !>          congruential sequence limited to small integers, and so
    !>          should produce machine independent random numbers. The
    !>          values of ISEED are changed on exit, and can be used in the
    !>          next call to CCHKST to continue the same random number
    !>          sequence.
    !>

    THRESH

    !>          THRESH is REAL
    !>          A test will count as  if the , computed as
    !>          described above, exceeds THRESH.  Note that the error
    !>          is scaled to be O(1), so THRESH should be a reasonably
    !>          small multiple of 1, e.g., 10 or 100.  In particular,
    !>          it should not depend on the precision (single vs. double)
    !>          or the size of the matrix.  It must be at least zero.
    !>

    NOUNIT

    !>          NOUNIT is INTEGER
    !>          The FORTRAN unit number for printing out error messages
    !>          (e.g., if a routine returns IINFO not equal to 0.)
    !>

    A

    !>          A is COMPLEX array of
    !>                                  dimension ( LDA , max(NN) )
    !>          Used to hold the matrix whose eigenvalues are to be
    !>          computed.  On exit, A contains the last matrix actually
    !>          used.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of A.  It must be at
    !>          least 1 and at least max( NN ).
    !>

    AP

    !>          AP is COMPLEX array of
    !>                      dimension( max(NN)*max(NN+1)/2 )
    !>          The matrix A stored in packed format.
    !>

    SD

    !>          SD is REAL array of
    !>                             dimension( max(NN) )
    !>          The diagonal of the tridiagonal matrix computed by CHETRD.
    !>          On exit, SD and SE contain the tridiagonal form of the
    !>          matrix in A.
    !>

    SE

    !>          SE is REAL array of
    !>                             dimension( max(NN) )
    !>          The off-diagonal of the tridiagonal matrix computed by
    !>          CHETRD.  On exit, SD and SE contain the tridiagonal form of
    !>          the matrix in A.
    !>

    D1

    !>          D1 is REAL array of
    !>                             dimension( max(NN) )
    !>          The eigenvalues of A, as computed by CSTEQR simultaneously
    !>          with Z.  On exit, the eigenvalues in D1 correspond with the
    !>          matrix in A.
    !>

    D2

    !>          D2 is REAL array of
    !>                             dimension( max(NN) )
    !>          The eigenvalues of A, as computed by CSTEQR if Z is not
    !>          computed.  On exit, the eigenvalues in D2 correspond with
    !>          the matrix in A.
    !>

    D3

    !>          D3 is REAL array of
    !>                             dimension( max(NN) )
    !>          The eigenvalues of A, as computed by SSTERF.  On exit, the
    !>          eigenvalues in D3 correspond with the matrix in A.
    !>

    D4

    !>          D4 is REAL array of
    !>                             dimension( max(NN) )
    !>          The eigenvalues of A, as computed by CPTEQR(V).
    !>          ZPTEQR factors S as  Z4 D4 Z4*
    !>          On exit, the eigenvalues in D4 correspond with the matrix in A.
    !>

    D5

    !>          D5 is REAL array of
    !>                             dimension( max(NN) )
    !>          The eigenvalues of A, as computed by ZPTEQR(N)
    !>          when Z is not computed. On exit, the
    !>          eigenvalues in D4 correspond with the matrix in A.
    !>

    WA1

    !>          WA1 is REAL array of
    !>                             dimension( max(NN) )
    !>          All eigenvalues of A, computed to high
    !>          absolute accuracy, with different range options.
    !>          as computed by SSTEBZ.
    !>

    WA2

    !>          WA2 is REAL array of
    !>                             dimension( max(NN) )
    !>          Selected eigenvalues of A, computed to high
    !>          absolute accuracy, with different range options.
    !>          as computed by SSTEBZ.
    !>          Choose random values for IL and IU, and ask for the
    !>          IL-th through IU-th eigenvalues.
    !>

    WA3

    !>          WA3 is REAL array of
    !>                             dimension( max(NN) )
    !>          Selected eigenvalues of A, computed to high
    !>          absolute accuracy, with different range options.
    !>          as computed by SSTEBZ.
    !>          Determine the values VL and VU of the IL-th and IU-th
    !>          eigenvalues and ask for all eigenvalues in this range.
    !>

    WR

    !>          WR is DOUBLE PRECISION array of
    !>                             dimension( max(NN) )
    !>          All eigenvalues of A, computed to high
    !>          absolute accuracy, with different options.
    !>          as computed by DSTEBZ.
    !>

    U

    !>          U is COMPLEX array of
    !>                             dimension( LDU, max(NN) ).
    !>          The unitary matrix computed by CHETRD + CUNGTR.
    !>

    LDU

    !>          LDU is INTEGER
    !>          The leading dimension of U, Z, and V.  It must be at least 1
    !>          and at least max( NN ).
    !>

    V

    !>          V is COMPLEX array of
    !>                             dimension( LDU, max(NN) ).
    !>          The Housholder vectors computed by CHETRD in reducing A to
    !>          tridiagonal form.  The vectors computed with UPLO='U' are
    !>          in the upper triangle, and the vectors computed with UPLO='L'
    !>          are in the lower triangle.  (As described in CHETRD, the
    !>          sub- and superdiagonal are not set to 1, although the
    !>          true Householder vector has a 1 in that position.  The
    !>          routines that use V, such as CUNGTR, set those entries to
    !>          1 before using them, and then restore them later.)
    !>

    VP

    !>          VP is COMPLEX array of
    !>                      dimension( max(NN)*max(NN+1)/2 )
    !>          The matrix V stored in packed format.
    !>

    TAU

    !>          TAU is COMPLEX array of
    !>                             dimension( max(NN) )
    !>          The Householder factors computed by CHETRD in reducing A
    !>          to tridiagonal form.
    !>

    Z

    !>          Z is COMPLEX array of
    !>                             dimension( LDU, max(NN) ).
    !>          The unitary matrix of eigenvectors computed by CSTEQR,
    !>          CPTEQR, and CSTEIN.
    !>

    WORK

    !>          WORK is COMPLEX array of
    !>                      dimension( LWORK )
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The number of entries in WORK.  This must be at least
    !>          1 + 4 * Nmax + 2 * Nmax * lg Nmax + 3 * Nmax**2
    !>          where Nmax = max( NN(j), 2 ) and lg = log base 2.
    !>

    IWORK

    !>          IWORK is INTEGER array,
    !>          Workspace.
    !>

    LIWORK

    !>          LIWORK is INTEGER
    !>          The number of entries in IWORK.  This must be at least
    !>                  6 + 6*Nmax + 5 * Nmax * lg Nmax
    !>          where Nmax = max( NN(j), 2 ) and lg = log base 2.
    !>

    RWORK

    !>          RWORK is REAL array
    !>

    LRWORK

    !>          LRWORK is INTEGER
    !>          The number of entries in LRWORK (dimension( ??? )
    !>

    RESULT

    !>          RESULT is REAL array, dimension (26)
    !>          The values computed by the tests described above.
    !>          The values are currently limited to 1/ulp, to avoid
    !>          overflow.
    !>

    INFO

    !>          INFO is INTEGER
    !>          If 0, then everything ran OK.
    !>           -1: NSIZES < 0
    !>           -2: Some NN(j) < 0
    !>           -3: NTYPES < 0
    !>           -5: THRESH < 0
    !>           -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
    !>          -23: LDU < 1 or LDU < NMAX.
    !>          -29: LWORK too small.
    !>          If  CLATMR, CLATMS, CHETRD, CUNGTR, CSTEQR, SSTERF,
    !>              or CUNMC2 returns an error code, the
    !>              absolute value of it is returned.
    !>
    !>-----------------------------------------------------------------------
    !>
    !>       Some Local Variables and Parameters:
    !>       ---- ----- --------- --- ----------
    !>       ZERO, ONE       Real 0 and 1.
    !>       MAXTYP          The number of types defined.
    !>       NTEST           The number of tests performed, or which can
    !>                       be performed so far, for the current matrix.
    !>       NTESTT          The total number of tests performed so far.
    !>       NBLOCK          Blocksize as returned by ENVIR.
    !>       NMAX            Largest value in NN.
    !>       NMATS           The number of matrices generated so far.
    !>       NERRS           The number of tests which have exceeded THRESH
    !>                       so far.
    !>       COND, IMODE     Values to be passed to the matrix generators.
    !>       ANORM           Norm of A; passed to matrix generators.
    !>
    !>       OVFL, UNFL      Overflow and underflow thresholds.
    !>       ULP, ULPINV     Finest relative precision and its inverse.
    !>       RTOVFL, RTUNFL  Square roots of the previous 2 values.
    !>               The following four arrays decode JTYPE:
    !>       KTYPE(j)        The general type (1-10) for type .
    !>       KMODE(j)        The MODE value to be passed to the matrix
    !>                       generator for type .
    !>       KMAGN(j)        The order of magnitude ( O(1),
    !>                       O(overflow^(1/2) ), O(underflow^(1/2) )
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 599 of file cchkst.f.

Author

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